## Active forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
- Application of Differential Equation: Newton's Law of Cooling

## New forum topics

- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
- Required diameter of solid shaft

## Recent comments

- 400000=120[14π(D2−10000)]

(…1 week 5 days ago - Use integration by parts for…1 month 1 week ago
- need answer1 month 1 week ago
- Yes you are absolutely right…1 month 1 week ago
- I think what is ask is the…1 month 1 week ago
- $\cos \theta = \dfrac{2}{…1 month 1 week ago
- Why did you use (1/SQ root 5…1 month 1 week ago
- How did you get the 300 000pi1 month 1 week ago
- It is not necessary to…1 month 2 weeks ago
- Draw a horizontal time line…1 month 2 weeks ago

## sin (x)=√2/4

ans. sin (x)=√2/4

solns:

tan(3x)=5tan(x) -----> eq. 1

tan(3x)=tan (2x + x)= (tan (2x)+tan(x))/(1-tan(2x)tan(x))-----> eq. 2

subs. 2 in 1

(tan (2x)+tan(x))/(1-tan(2x)tan(x))=5tan(x)

tan(2x) + tan (x)=5tan(x)-5tan(2x)tan

^{2}(x)tan(2x)=4tan(x)-5tan(2x)tan

^{2}(x)tan(2x)+5tan(2x)tan

^{2}(x)=4tan(x)tan(2x)(1 + 5tan

^{2}(x)=4tan(x)----- eq. 3tan(2x)=2tan(x)/(1-tan

^{2}(x)) -----eq.4substitute 4 to 3

2tan(x) (1 + 5tan

^{2}(x))/(1-tan^{2}(x)) =4tan(x)2tan(x) (1 + 5tan

^{2}(x))=4tan(x)(1-tan^{2}(x))2tan(x) + 10tan

^{3}(x))=4tan(x)-4tan^{3}(x)14tan

^{3}(x)=2tan(x)14(sin

^{3}(x)/cos^{3}(x))=2(sin(x)/cos(x))14(sin

^{2}(x)/cos^{2}(x))=214sin

^{2}(x)=2cos^{2}(x)14sin

^{2}(x)=2(1-sin^{2}(x))14sin

^{2}(x)+2sin^{2}(x)=216sin

^{2}(x)=2sin(x)=√(2/16) or

sin (x)=√2/4 ans.

where x=20.705

^{o}## $yehey$

$yehey$